de thi lai toan 10

[r]

S6'Giao due va Dao tao Tp.HCM

DE KIEM TRA L~I NA.M HQC 2011 - 2012

MON ToAN LOP 10 Thoi gian: 90 phut

CaD 1: (3 diem)

Giai cac b~t plurong trinh sau:

2

a) x -4x+3 <1 b) 3x 2 -15x-21 >a

CaD2: (2 diem)

CaD3: (3 diem)

CaD4: (2 diem)

1

nET

DAp AN DE KIEM TRA L~I LOP 10 Call 1:

1)

a <¢::> <

¢::>x(x - 2) <0 (0,2Sd)

3-2x

¢::>x E(0;%)U(2;-too) (O,Sd)

b) 3x2 -ISx - 21>0¢::>3x2 > ISx - 21 (O,2Sd)

¢::>(3x2 - Sx+2)(3x2 +5x - 2) >0 (O,2Sd)

¢::>x E(-OO;-2)U(±;~)U(1;-too) (O,Sd)

(O,2Sd)

lx;::::1

c) .J 2x+l <x-I¢::> x;:::: ¢ >{ 2 ¢::>{ - 0¢::>x>4 (O,2Sdx4)

2x+l «x - l)2

Call 2: Xet b~t phuong trinh: (m -1)x2 +2x-1::; 0 (*)

a) m= -1: (*) ¢::>_2x2 +2x-1::; 0¢ >'IIxER (O,Sd)

b) NSu m = 1 thi (*)¢::>x::;! => m = 1 khong thoa man (O,Sd)

2

• N~u m " *1 thi (*) dung voi 'IIxE R ¢::>{m,-1 < 0 (O,Sd) ¢::>m ~ °(O,Sd)

Ll =1+m-l::;O

Call 3 : Trong h~ true toa d9 Oxy, eho dirong trim (C): (x _1)2 + (y - 2)2 =8

a) Tam 1(1; 2) (O,Sd), ban kinh R = 2Ji (O,Sd)

b) ViSt phirong trinh dirong thang !l qua I, song song voi dirong thang d:x - y - 1= °

• !l//d nen phuong trinh !lco dang x - y + C =0 (C"* -1) (O,2Sd)

• !l di qua I nen co 1- 2 + C =0¢::>C =1 (O,Sd) = PT zl : x - y +1= 0 (O,2Sd)

c) ViSt phirong trinh tiSp tuyen cua (C ) vuong goc voi !l

.TiSp tuyen L\vuong goc voi !l nen PTTT co dang x + y + D =0 (O,2Sd)

va d(l, L \) =R¢::>11;2+ DI= J8(O,2Sd)

\'12 + 12

¢::>(D + 3)2 =16¢::>[D =-7 (O,Sd)

D=l

V~y PT cac tiSp tuyen dn tim: x+y+l =0, x+ y-7 =O

Call 4:

) Ch 3 T' h , , b· ;: h 'A 2 sina 1

a 0 tan a = In gia tn eua leu t irc : = +

2sina 1 2tana 2

A= + = + tan a + 1 (O,75d) = 16 (O,25d) sina-2cosa cos2a tana-2

b) Cho a=b =; Tinh gia tri bi~u thirc: B=(cosa-2cosb ) 2 +(sina-2sinb)2

B =( cosa - 2cosb)2 + (sin a - 2sinb)2 =5 -4(cosacosb +sinasin b )(O,5d)

Tr

=5 -4cos ( a - b ) =5 -4cos- =3 (O,5d)

3